You can password protect .pst files in Outlook. The way to do this is to create an encrypted .pst file. This is the point at which you can then add a password. You can add a password to unencrypted .pst, but the security is very low. You can even use an option called compressible encryption if you want to.

You can then drag emails and/or folders from the unencrypted .pst file to the encrypted one. Note that Outlook will do a move operation, not a copy.

And to anyone that wishes to challenge me on this, I work with Outlook every day in my job, so I know this very well!